Question: Simplify the following expression: $r = \dfrac{-7p^2 + 63p}{-42p^2 - 63p}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-7p^2 + 63p = - (7 \cdot p \cdot p) + (3\cdot3\cdot7 \cdot p)$ The denominator can be factored: $-42p^2 - 63p = - (2\cdot3\cdot7 \cdot p \cdot p) - (3\cdot3\cdot7 \cdot p)$ The greatest common factor of all the terms is $7p$ Factoring out $7p$ gives us: $r = \dfrac{(7p)(-p + 9)}{(7p)(-6p - 9)}$ Dividing both the numerator and denominator by $7p$ gives: $r = \dfrac{-p + 9}{-6p - 9}$